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<link title="Index of types" rel=Appendix href="index_types.html">
<link title="Index of values" rel=Appendix href="index_values.html">
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<link title="Fpu" rel="Chapter" href="Fpu.html">
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<link title="Interval" rel="Chapter" href="Interval.html"><title>Index of values</title>
</head>
<body>
<center><h1>Index of values</h1></center>
<table>
<tr><td align="left"><br></td></tr>
<tr><td><a href="Interval.html#VAL( *$ )">( *$ )</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">a *$ b</code>
multiplies <code class="code">a</code> by <code class="code">b</code> according to interval arithmetic and returns the proper result.
</div>
</td></tr>
<tr><td><a href="Interval.html#VAL( *$. )">( *$. )</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">a *$. x</code> multiplies <code class="code">a</code> by <code class="code">x</code> according to interval arithmetic and returns the proper result.
</div>
</td></tr>
<tr><td><a href="Fpu_rename_all.html#VAL( ** )">( ** )</a> [<a href="Fpu_rename_all.html">Fpu_rename_all</a>]</td>
<td><div class="info">
Computes x^y
</div>
</td></tr>
<tr><td><a href="Fpu_rename.html#VAL( ** )">( ** )</a> [<a href="Fpu_rename.html">Fpu_rename</a>]</td>
<td><div class="info">
Computes x^y
</div>
</td></tr>
<tr><td><a href="Interval.html#VAL( **$ )">( **$ )</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">a **$ b</code> returns interval <code class="code">a</code> raised to <code class="code">b</code> power according to interval arithmetic, considering the restriction of x power y to x &gt;= 0.
</div>
</td></tr>
<tr><td><a href="Interval.html#VAL( **$. )">( **$. )</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">a **$. f</code> returns interval <code class="code">a</code> raised to f power according to interval arithmetic.
</div>
</td></tr>
<tr><td><a href="Interval.html#VAL( **.$ )">( **.$ )</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">x **.$ a</code> returns float <code class="code">x</code> raised to interval <code class="code">a</code> power according to interval arithmetic, considering the restiction of x power y to x &gt;= 0.
</div>
</td></tr>
<tr><td><a href="Fpu_rename_all.html#VAL( *. )">( *. )</a> [<a href="Fpu_rename_all.html">Fpu_rename_all</a>]</td>
<td><div class="info">
Computes x * y
</div>
</td></tr>
<tr><td><a href="Interval.html#VAL( *.$ )">( *.$ )</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">x *$. a</code> multiplies <code class="code">a</code> by <code class="code">x</code> according to interval arithmetic and returns the proper result.
</div>
</td></tr>
<tr><td><a href="Interval.html#VAL(+$)">(+$)</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">a +$ b</code> returns <code class="code">{low=a.low+.b.low;high=a.high+.b.high}</code>
</div>
</td></tr>
<tr><td><a href="Interval.html#VAL(+$.)">(+$.)</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">a +$. x</code> returns <code class="code">{low=a.low+.x;high=a.high+.x}</code>
</div>
</td></tr>
<tr><td><a href="Interval.html#VAL(+.$)">(+.$)</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">x +.$ a</code> returns <code class="code">{low=a.low+.x;high=a.high+.x}</code>
</div>
</td></tr>
<tr><td><a href="Fpu_rename_all.html#VAL(+.)">(+.)</a> [<a href="Fpu_rename_all.html">Fpu_rename_all</a>]</td>
<td><div class="info">
Computes x + y
</div>
</td></tr>
<tr><td><a href="Interval.html#VAL(-$)">(-$)</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">a -$ b</code> returns <code class="code">{low=a.low-.b.high;high=a.high-.b.low}</code>
</div>
</td></tr>
<tr><td><a href="Interval.html#VAL(-$.)">(-$.)</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">a -$. x</code> returns <code class="code">{low=a.low-.x;high=a.high-.x}</code>
</div>
</td></tr>
<tr><td><a href="Interval.html#VAL(-.$)">(-.$)</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">x -.$ a</code> returns <code class="code">{low=x-.a.high;high=x-.a.low}</code>
</div>
</td></tr>
<tr><td><a href="Fpu_rename_all.html#VAL(-.)">(-.)</a> [<a href="Fpu_rename_all.html">Fpu_rename_all</a>]</td>
<td><div class="info">
Computes x - y
</div>
</td></tr>
<tr><td><a href="Interval.html#VAL(/$)">(/$)</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">a /$ b</code> divides the first interval by the second according to interval arithmetic and returns the proper result.
</div>
</td></tr>
<tr><td><a href="Interval.html#VAL(/$.)">(/$.)</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">a /$. x</code> divides <code class="code">a</code> by <code class="code">x</code> according to interval arithmetic and returns the proper result.
</div>
</td></tr>
<tr><td><a href="Interval.html#VAL(/.$)">(/.$)</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">x /.$ a</code> divides <code class="code">x</code> by <code class="code">a</code> according to interval arithmetic and returns the result.
</div>
</td></tr>
<tr><td><a href="Fpu_rename_all.html#VAL(/.)">(/.)</a> [<a href="Fpu_rename_all.html">Fpu_rename_all</a>]</td>
<td><div class="info">
Computes x / y
</div>
</td></tr>
<tr><td><a href="Interval.html#VAL(<$.)">(&lt;$.)</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
Deprecated
</div>
</td></tr>
<tr><td><a href="Interval.html#VAL(~-$)">(~-$)</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">~-$ a</code> returns <code class="code">{low=-a.high;high=-a.low}</code>
</div>
</td></tr>
<tr><td align="left"><br>A</td></tr>
<tr><td><a href="Interval.html#VALabs_I">abs_I</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">abs_I a</code> returns <code class="code">{low=a.low;high=a.high}</code> if <code class="code">a.low&gt;=0.</code>, <code class="code">{low=-a.high;high=-a.low}</code> if <code class="code">a.high&lt;=0.</code>, and <code class="code">{low=0.;high=max -a.low a.high}</code>
otherwise
</div>
</td></tr>
<tr><td><a href="Fpu_rename_all.html#VALacos">acos</a> [<a href="Fpu_rename_all.html">Fpu_rename_all</a>]</td>
<td><div class="info">
arc-cosine function
</div>
</td></tr>
<tr><td><a href="Fpu_rename.html#VALacos">acos</a> [<a href="Fpu_rename.html">Fpu_rename</a>]</td>
<td><div class="info">
arc-cosine function
</div>
</td></tr>
<tr><td><a href="Interval.html#VALacos_I">acos_I</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">acos_I a</code> raise <code class="code">Failure "acos_I"</code> if <code class="code">a.low&gt;1. or a.high&lt;-1.</code>, else returns <code class="code">{low=if a.high&lt;1. then acos a.high else 0; high=if a.low&gt;-1. then acos a.low else pi}</code>.
</div>
</td></tr>
<tr><td><a href="Fpu_rename_all.html#VALasin">asin</a> [<a href="Fpu_rename_all.html">Fpu_rename_all</a>]</td>
<td><div class="info">
arc-sinus function
</div>
</td></tr>
<tr><td><a href="Fpu_rename.html#VALasin">asin</a> [<a href="Fpu_rename.html">Fpu_rename</a>]</td>
<td><div class="info">
arc-sinus function
</div>
</td></tr>
<tr><td><a href="Interval.html#VALasin_I">asin_I</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">asin_I a</code> raise <code class="code">Failure "asin_I"</code> if <code class="code">a.low&gt;1. or a.high&lt;-1.</code> else returns <code class="code">{low=if a.low&gt;-1. then asin a.low else -pi/2; high=if a.low&lt;1. then asin a.high else pi/2}</code>.
</div>
</td></tr>
<tr><td><a href="Fpu_rename_all.html#VALatan">atan</a> [<a href="Fpu_rename_all.html">Fpu_rename_all</a>]</td>
<td><div class="info">
arc-tan function
</div>
</td></tr>
<tr><td><a href="Fpu_rename.html#VALatan">atan</a> [<a href="Fpu_rename.html">Fpu_rename</a>]</td>
<td><div class="info">
arc-tan function
</div>
</td></tr>
<tr><td><a href="Fpu_rename_all.html#VALatan2">atan2</a> [<a href="Fpu_rename_all.html">Fpu_rename_all</a>]</td>
<td><div class="info">
atan2 function
</div>
</td></tr>
<tr><td><a href="Fpu_rename.html#VALatan2">atan2</a> [<a href="Fpu_rename.html">Fpu_rename</a>]</td>
<td><div class="info">
atan2 function
</div>
</td></tr>
<tr><td><a href="Interval.html#VALatan2_I_I">atan2_I_I</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
Same function as above but when y.low&lt;0 and y.high&gt;0 and x.high&lt;0 the returned interval is [-pi,pi].
</div>
</td></tr>
<tr><td><a href="Interval.html#VALatan2mod_I_I">atan2mod_I_I</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">atan2mod_I_I y x</code> returns the proper extension of interval arithmetic to atan2 but with values in [-pi,2 pi] instead of [-pi,pi].
</div>
</td></tr>
<tr><td><a href="Interval.html#VALatan_I">atan_I</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">atan_I a</code>  returns <code class="code">{low=atan a.low;high=atan a.high}</code>
</div>
</td></tr>
<tr><td align="left"><br>C</td></tr>
<tr><td><a href="Interval.html#VALcompare_I_f">compare_I_f</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">compare_I_f a x</code> returns <code class="code">1</code> if <code class="code">a.high&lt;x</code>, <code class="code">0</code> if <code class="code">a.low&lt;=x&lt;=a.high</code> and <code class="code">-1</code> if  <code class="code">x&lt;a.low</code>
</div>
</td></tr>
<tr><td><a href="Fpu_rename_all.html#VALcos">cos</a> [<a href="Fpu_rename_all.html">Fpu_rename_all</a>]</td>
<td><div class="info">
Computes cos(x) for x in [-2^63, 2^63]
</div>
</td></tr>
<tr><td><a href="Fpu_rename.html#VALcos">cos</a> [<a href="Fpu_rename.html">Fpu_rename</a>]</td>
<td><div class="info">
Computes cos(x) for x in [-2^63, 2^63]
</div>
</td></tr>
<tr><td><a href="Interval.html#VALcos_I">cos_I</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">cos_I a</code>  returns the proper extension of cos to arithmetic interval 
Returns [-1,1] if one of the bounds is greater or lower than +/-2**53
</div>
</td></tr>
<tr><td><a href="Fpu_rename_all.html#VALcosh">cosh</a> [<a href="Fpu_rename_all.html">Fpu_rename_all</a>]</td>
<td><div class="info">
cosh function
</div>
</td></tr>
<tr><td><a href="Fpu_rename.html#VALcosh">cosh</a> [<a href="Fpu_rename.html">Fpu_rename</a>]</td>
<td><div class="info">
cosh function
</div>
</td></tr>
<tr><td><a href="Interval.html#VALcosh_I">cosh_I</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
cosh_I is the proper extension of interval arithmetic to cosh
</div>
</td></tr>
<tr><td align="left"><br>E</td></tr>
<tr><td><a href="Interval.html#VALe_I">e_I</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">e</code> with bounds properly rounded
</div>
</td></tr>
<tr><td><a href="Fpu_rename_all.html#VALexp">exp</a> [<a href="Fpu_rename_all.html">Fpu_rename_all</a>]</td>
<td><div class="info">
exp function
</div>
</td></tr>
<tr><td><a href="Fpu_rename.html#VALexp">exp</a> [<a href="Fpu_rename.html">Fpu_rename</a>]</td>
<td><div class="info">
exp function
</div>
</td></tr>
<tr><td><a href="Interval.html#VALexp_I">exp_I</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">exp_I a</code> returns <code class="code">{low=exp a.high;high=exp b.high}</code>
</div>
</td></tr>
<tr><td align="left"><br>F</td></tr>
<tr><td><a href="Fpu.html#VALfacos">facos</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALfacos_high">facos_high</a> [<a href="Fpu.html">Fpu</a>]</td>
<td><div class="info">
arc-cosine functions
</div>
</td></tr>
<tr><td><a href="Fpu.html#VALfacos_low">facos_low</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALfadd">fadd</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALfadd_high">fadd_high</a> [<a href="Fpu.html">Fpu</a>]</td>
<td><div class="info">
Floating point addition in nearest, low and high mode
</div>
</td></tr>
<tr><td><a href="Fpu.html#VALfadd_low">fadd_low</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALfasin">fasin</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALfasin_high">fasin_high</a> [<a href="Fpu.html">Fpu</a>]</td>
<td><div class="info">
arc-sinus functions
</div>
</td></tr>
<tr><td><a href="Fpu.html#VALfasin_low">fasin_low</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALfatan">fatan</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALfatan_high">fatan_high</a> [<a href="Fpu.html">Fpu</a>]</td>
<td><div class="info">
fatan x y computes atan2 y x
</div>
</td></tr>
<tr><td><a href="Fpu.html#VALfatan_low">fatan_low</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALfcos">fcos</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALfcos_high">fcos_high</a> [<a href="Fpu.html">Fpu</a>]</td>
<td><div class="info">
Computes cos(x) for x in ]-2^63, 2^63[
</div>
</td></tr>
<tr><td><a href="Fpu.html#VALfcos_low">fcos_low</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALfcosh">fcosh</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALfcosh_high">fcosh_high</a> [<a href="Fpu.html">Fpu</a>]</td>
<td><div class="info">
Computes cosh(x)
</div>
</td></tr>
<tr><td><a href="Fpu.html#VALfcosh_low">fcosh_low</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALfdiv">fdiv</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALfdiv_high">fdiv_high</a> [<a href="Fpu.html">Fpu</a>]</td>
<td><div class="info">
Floating point division in nearest, low and high mode
</div>
</td></tr>
<tr><td><a href="Fpu.html#VALfdiv_low">fdiv_low</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALfexp">fexp</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALfexp_high">fexp_high</a> [<a href="Fpu.html">Fpu</a>]</td>
<td><div class="info">
Floating point exponential in nearest, low and high mode
</div>
</td></tr>
<tr><td><a href="Fpu.html#VALfexp_low">fexp_low</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALffloat">ffloat</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALffloat_high">ffloat_high</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALffloat_low">ffloat_low</a> [<a href="Fpu.html">Fpu</a>]</td>
<td><div class="info">
float() functions.
</div>
</td></tr>
<tr><td><a href="Interval.html#VALfloat_i">float_i</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
Returns the interval containing the float conversion of an integer
</div>
</td></tr>
<tr><td><a href="Fpu.html#VALflog">flog</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALflog_high">flog_high</a> [<a href="Fpu.html">Fpu</a>]</td>
<td><div class="info">
Floating point log in nearest, low and high mode
</div>
</td></tr>
<tr><td><a href="Fpu.html#VALflog_low">flog_low</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALflog_pow">flog_pow</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALflog_pow_high">flog_pow_high</a> [<a href="Fpu.html">Fpu</a>]</td>
<td><div class="info">
Computes x^y for 0 &lt; x &lt; infinity and neg_infinity &lt; y &lt; infinity
</div>
</td></tr>
<tr><td><a href="Fpu.html#VALflog_pow_low">flog_pow_low</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALfmod">fmod</a> [<a href="Fpu.html">Fpu</a>]</td>
<td><div class="info">
Modulo (result is supposed to be exact)
</div>
</td></tr>
<tr><td><a href="Fpu.html#VALfmul">fmul</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALfmul_high">fmul_high</a> [<a href="Fpu.html">Fpu</a>]</td>
<td><div class="info">
Floating point multiplication in nearest, low and high mode
</div>
</td></tr>
<tr><td><a href="Fpu.html#VALfmul_low">fmul_low</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALfpow">fpow</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALfpow_high">fpow_high</a> [<a href="Fpu.html">Fpu</a>]</td>
<td><div class="info">
Computes x^y expanded to its mathematical limit when it exists
</div>
</td></tr>
<tr><td><a href="Fpu.html#VALfpow_low">fpow_low</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Interval.html#VALfprintf_I">fprintf_I</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
Prints an interval into an out_channel with the same format applied to both endpoints
</div>
</td></tr>
<tr><td><a href="Interval.html#VALfprintf_X">fprintf_X</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
Prints an interval vector into an out_channel 
with the same format applied to all endpoints
</div>
</td></tr>
<tr><td><a href="Fpu.html#VALfsin">fsin</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALfsin_high">fsin_high</a> [<a href="Fpu.html">Fpu</a>]</td>
<td><div class="info">
Computes sin(x) for x in ]-2^63, 2^63[
</div>
</td></tr>
<tr><td><a href="Fpu.html#VALfsin_low">fsin_low</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALfsinh">fsinh</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALfsinh_high">fsinh_high</a> [<a href="Fpu.html">Fpu</a>]</td>
<td><div class="info">
Computes sinh(x)
</div>
</td></tr>
<tr><td><a href="Fpu.html#VALfsinh_low">fsinh_low</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALfsqrt">fsqrt</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALfsqrt_high">fsqrt_high</a> [<a href="Fpu.html">Fpu</a>]</td>
<td><div class="info">
Floating point square root in nearest, low and high mode
</div>
</td></tr>
<tr><td><a href="Fpu.html#VALfsqrt_low">fsqrt_low</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALfsub">fsub</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALfsub_high">fsub_high</a> [<a href="Fpu.html">Fpu</a>]</td>
<td><div class="info">
Floating point substraction in nearest, low and high mode
</div>
</td></tr>
<tr><td><a href="Fpu.html#VALfsub_low">fsub_low</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALftan">ftan</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALftan_high">ftan_high</a> [<a href="Fpu.html">Fpu</a>]</td>
<td><div class="info">
Computes tan(x) for x in ]-2^63, 2^63[
</div>
</td></tr>
<tr><td><a href="Fpu.html#VALftan_low">ftan_low</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALftanh">ftanh</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td><a href="Fpu.html#VALftanh_high">ftanh_high</a> [<a href="Fpu.html">Fpu</a>]</td>
<td><div class="info">
Computes tanh(x)
</div>
</td></tr>
<tr><td><a href="Fpu.html#VALftanh_low">ftanh_low</a> [<a href="Fpu.html">Fpu</a>]</td>
<td></td></tr>
<tr><td align="left"><br>I</td></tr>
<tr><td><a href="Interval.html#VALinv_I">inv_I</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">inv_I a</code> returns <code class="code">1. /.$ a</code>.
</div>
</td></tr>
<tr><td><a href="Fpu.html#VALis_neg">is_neg</a> [<a href="Fpu.html">Fpu</a>]</td>
<td><div class="info">
is_neg x returns if x has its sign bit set (true for -0.)
</div>
</td></tr>
<tr><td align="left"><br>L</td></tr>
<tr><td><a href="Fpu_rename_all.html#VALlog">log</a> [<a href="Fpu_rename_all.html">Fpu_rename_all</a>]</td>
<td><div class="info">
log function
</div>
</td></tr>
<tr><td><a href="Fpu_rename.html#VALlog">log</a> [<a href="Fpu_rename.html">Fpu_rename</a>]</td>
<td><div class="info">
log function
</div>
</td></tr>
<tr><td><a href="Interval.html#VALlog_I">log_I</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">log_I a</code> returns <code class="code">{low=log a.low; high=log a.high}</code> if <code class="code">a.low&gt;0.</code>, <code class="code">{low=neg_infinity; high=log a.high}</code> if <code class="code">a.low&lt;0&lt;=a.high</code>.
</div>
</td></tr>
<tr><td align="left"><br>M</td></tr>
<tr><td><a href="Interval.html#VALmax_I_I">max_I_I</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">max_I_I a b</code> returns <code class="code">{low=max a.low b.low;high=max a.high b.high}</code>
</div>
</td></tr>
<tr><td><a href="Interval.html#VALmin_I_I">min_I_I</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">min_I_I a b</code> returns <code class="code">{low=min a.low b.low;high=min a.high b.high}</code>
</div>
</td></tr>
<tr><td><a href="Interval.html#VALmod_I_f">mod_I_f</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">mod_I_f a f</code> returns <code class="code">a</code> mod <code class="code">f</code> according to interval arithmetic et ocaml mod_float definition.
</div>
</td></tr>
<tr><td><a href="Fpu_rename_all.html#VALmod_float">mod_float</a> [<a href="Fpu_rename_all.html">Fpu_rename_all</a>]</td>
<td><div class="info">
Computes x mod y
</div>
</td></tr>
<tr><td><a href="Fpu_rename.html#VALmod_float">mod_float</a> [<a href="Fpu_rename.html">Fpu_rename</a>]</td>
<td><div class="info">
Computes x mod y
</div>
</td></tr>
<tr><td align="left"><br>O</td></tr>
<tr><td><a href="Interval.html#VALone_I">one_I</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
Neutral element for multiplication
</div>
</td></tr>
<tr><td align="left"><br>P</td></tr>
<tr><td><a href="Interval.html#VALpi_I">pi_I</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">pi</code> with bounds properly rounded
</div>
</td></tr>
<tr><td><a href="Interval.html#VALpow_I_I">pow_I_I</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
Deprecated
</div>
</td></tr>
<tr><td><a href="Interval.html#VALpow_I_f">pow_I_f</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
Deprecated
</div>
</td></tr>
<tr><td><a href="Interval.html#VALpow_I_i">pow_I_i</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">Pow_I_i a n</code> with <code class="code">n</code> integer returns interval <code class="code">a</code> raised to nth power according to interval arithmetic.
</div>
</td></tr>
<tr><td><a href="Interval.html#VALprint_I">print_I</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
Deprecated
</div>
</td></tr>
<tr><td><a href="Interval.html#VALprint_X">print_X</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
Deprecated
</div>
</td></tr>
<tr><td><a href="Interval.html#VALprintf_I">printf_I</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
Prints an interval with the same format applied to both endpoints.
</div>
</td></tr>
<tr><td><a href="Interval.html#VALprintf_X">printf_X</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
Prints an interval vector with the same format applied to all endpoints.
</div>
</td></tr>
<tr><td align="left"><br>S</td></tr>
<tr><td><a href="Fpu.html#VALset_high">set_high</a> [<a href="Fpu.html">Fpu</a>]</td>
<td><div class="info">
Sets the rounding mod to UPWARD (towards infinity)
</div>
</td></tr>
<tr><td><a href="Fpu.html#VALset_low">set_low</a> [<a href="Fpu.html">Fpu</a>]</td>
<td><div class="info">
Sets the rounding mod to DOWNWARD (towards minus infinity)
</div>
</td></tr>
<tr><td><a href="Fpu.html#VALset_nearest">set_nearest</a> [<a href="Fpu.html">Fpu</a>]</td>
<td><div class="info">
Sets the rounding mod to NEAREST (default mode)
</div>
</td></tr>
<tr><td><a href="Interval.html#VALsgn_I">sgn_I</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">sgn_I a</code> returns <code class="code">{low=float (compare a.low 0.);high=float (compare a.high 0.)}</code>
</div>
</td></tr>
<tr><td><a href="Fpu_rename_all.html#VALsin">sin</a> [<a href="Fpu_rename_all.html">Fpu_rename_all</a>]</td>
<td><div class="info">
Computes sin(x) for x in [-2^63, 2^63]
</div>
</td></tr>
<tr><td><a href="Fpu_rename.html#VALsin">sin</a> [<a href="Fpu_rename.html">Fpu_rename</a>]</td>
<td><div class="info">
Computes sin(x) for x in [-2^63, 2^63]
</div>
</td></tr>
<tr><td><a href="Interval.html#VALsin_I">sin_I</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">sin_I a</code>  returns the proper extension of sin to arithmetic interval
Returns [-1,1] if one of the bounds is greater or lower than +/-2**53
</div>
</td></tr>
<tr><td><a href="Fpu_rename_all.html#VALsinh">sinh</a> [<a href="Fpu_rename_all.html">Fpu_rename_all</a>]</td>
<td><div class="info">
sinh function
</div>
</td></tr>
<tr><td><a href="Fpu_rename.html#VALsinh">sinh</a> [<a href="Fpu_rename.html">Fpu_rename</a>]</td>
<td><div class="info">
sinh function
</div>
</td></tr>
<tr><td><a href="Interval.html#VALsinh_I">sinh_I</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
sinh_I is the proper extension of interval arithmetic to sinh
</div>
</td></tr>
<tr><td><a href="Interval.html#VALsize2_X">size2_X</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
Deprecated
</div>
</td></tr>
<tr><td><a href="Interval.html#VALsize_I">size_I</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">size_I a</code> returns <code class="code">a.high-a.low</code>
</div>
</td></tr>
<tr><td><a href="Interval.html#VALsize_X">size_X</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
Deprecated
</div>
</td></tr>
<tr><td><a href="Interval.html#VALsize_max_X">size_max_X</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
Computes the size of the largest interval of the interval vector
</div>
</td></tr>
<tr><td><a href="Interval.html#VALsize_mean_X">size_mean_X</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
Computes the mean of the size of intervals of the interval vector
</div>
</td></tr>
<tr><td><a href="Interval.html#VALsprintf_I">sprintf_I</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
Returns a string holding the interval printed with the same format applied to both 
endpoints
</div>
</td></tr>
<tr><td><a href="Interval.html#VALsprintf_X">sprintf_X</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
Returns a string holding the interval vector printed with the same format applied to all
endpoints
</div>
</td></tr>
<tr><td><a href="Fpu_rename_all.html#VALsqrt">sqrt</a> [<a href="Fpu_rename_all.html">Fpu_rename_all</a>]</td>
<td><div class="info">
square root function
</div>
</td></tr>
<tr><td><a href="Fpu_rename.html#VALsqrt">sqrt</a> [<a href="Fpu_rename.html">Fpu_rename</a>]</td>
<td><div class="info">
square root function
</div>
</td></tr>
<tr><td><a href="Interval.html#VALsqrt_I">sqrt_I</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">sqrt_I a</code> returns <code class="code">{low=sqrt a;high=sqrt b}</code> if <code class="code">a&gt;=0.</code>, <code class="code">{low=0.;high=sqrt b}</code> if <code class="code">a&lt;0.&lt;=b</code>.
</div>
</td></tr>
<tr><td align="left"><br>T</td></tr>
<tr><td><a href="Fpu_rename_all.html#VALtan">tan</a> [<a href="Fpu_rename_all.html">Fpu_rename_all</a>]</td>
<td><div class="info">
Computes tan(x) for x in [-2^63, 2^63]
</div>
</td></tr>
<tr><td><a href="Fpu_rename.html#VALtan">tan</a> [<a href="Fpu_rename.html">Fpu_rename</a>]</td>
<td><div class="info">
Computes tan(x) for x in [-2^63, 2^63]
</div>
</td></tr>
<tr><td><a href="Interval.html#VALtan_I">tan_I</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">tan_I a</code>  returns the proper extension of tan to arithmetic interval 
Returns [-Inf,Inf] if one of the bounds is greater or lower than +/-2**53
</div>
</td></tr>
<tr><td><a href="Fpu_rename_all.html#VALtanh">tanh</a> [<a href="Fpu_rename_all.html">Fpu_rename_all</a>]</td>
<td><div class="info">
tanh function
</div>
</td></tr>
<tr><td><a href="Fpu_rename.html#VALtanh">tanh</a> [<a href="Fpu_rename.html">Fpu_rename</a>]</td>
<td><div class="info">
tanh function
</div>
</td></tr>
<tr><td><a href="Interval.html#VALtanh_I">tanh_I</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
tanh_I is the proper extension of interval arithmetic to tanh
</div>
</td></tr>
<tr><td><a href="Interval.html#VALtruncate_I">truncate_I</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">truncate_I a</code> returns <code class="code">{low=floor a.low;high=ceil a.high}</code>
</div>
</td></tr>
<tr><td align="left"><br>U</td></tr>
<tr><td><a href="Interval.html#VALunion_I_I">union_I_I</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
<code class="code">union_I_I a b</code> returns <code class="code">{low=min a.low b.low;high=max a.high b.high}</code>
</div>
</td></tr>
<tr><td align="left"><br>Z</td></tr>
<tr><td><a href="Interval.html#VALzero_I">zero_I</a> [<a href="Interval.html">Interval</a>]</td>
<td><div class="info">
Neutral element for addition
</div>
</td></tr>
</table><br>
</body>
</html>